Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 852 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 11 (c) 60 (d) 30
2. 2.In which quadrant does the point (5, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
3. 3.A bag has 7 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 8 (c) 2 (d) 14
4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
5. 5.In a class of 33 children, 15 like dance, 25 like music and 10 like both. How many like at least one of the two? (a) 20 (b) 33 (c) 40 (d) 30
6. 6.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
7. 7.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
8. 8.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 245° (d) 130°
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 1/9 (c) 4/11 (d) 5/36
10. 10.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 320° (c) 50° (d) 140°
11. 11.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 75°
12. 12.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
13. 13.What is the 23rd term of the AP 11, 15, 19, 23, …? (a) 88 (b) 99 (c) 92 (d) 103
14. 14.What is the midpoint of the line joining (6, 5) and (14, 1)? (a) (3, 10) (b) (20, 6) (c) (10, 3) (d) (4, 2)
15. 15.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 14 (c) 21 (d) 22
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
17. 17.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
18. 18.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 30° (d) 120°
19. 19.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
20. 20.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 65° (d) 115°
21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 5 (d) 3
22. 22.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 961 (b) 971 (c) 901 (d) 841
23. 23.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 15 (d) 36
24. 24.In a class of 23 children, 15 like cricket, 15 like football and 11 like both. How many like neither? (a) 11 (b) 15 (c) 5 (d) 4
25. 25.A bag has 12 red balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 13 (c) 17 (d) 2
26. 26.What is the mode of 6, 4, 4, 6, 4, 12 and 20? (a) 12 (b) 20 (c) 4 (d) 6
27. 27.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 154 (c) 133 (d) 266
28. 28.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 21 (b) 19 (c) 26 (d) 20
29. 29.A bag has 8 green, 9 blue and 6 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 8/23 (b) 16/23 (c) 15/23 (d) 1/3
30. 30.A drawer has lots of red, green and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 4 (d) 3
31. 31.A drawer has lots of black, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 6 (d) 3
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
33. 33.A bag has 7 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 8 (d) 9
34. 34.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
35. 35.What is the midpoint of the line joining (7, 9) and (15, 17)? (a) (22, 26) (b) (11, 13) (c) (4, 4) (d) (13, 11)
36. 36.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 36 (d) 28
37. 37.In a class of 40 children, 21 like maths, 21 like science and 9 like neither. How many like both? (a) 31 (b) 9 (c) 2 (d) 11
38. 38.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 95° (b) 105° (c) 75° (d) 160°
39. 39.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 15 (d) 7
40. 40.What is the midpoint of the line joining (3, 2) and (5, 4)? (a) (3, 4) (b) (1, 1) (c) (4, 3) (d) (8, 6)

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad